In this paper we consider the so-called procedure of {it Continuous Steiner Symmetrization}, introduced by Brock in~cite{bro95,bro00}. It transforms every open set $OmegacompR^d$ into the ball keeping the volume fixed and letting the first eigenvalue and the torsional rigidity respectively decrease and increase. While this does not provide, in general, a $gamma$-continuous map $tmapstoOmega_t$, it can be slightly modified so to obtain the $gamma$-continuity for a $gamma$-dense class of domains $Omega$, namely, the class of polyhedral sets in $R^d$. This allows to obtain a sharp characterization of the Blaschke-Santal'o diagram of torsion and eigenvalue.

An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams

Giuseppe Buttazzo;Aldo Pratelli
2021-01-01

Abstract

In this paper we consider the so-called procedure of {it Continuous Steiner Symmetrization}, introduced by Brock in~cite{bro95,bro00}. It transforms every open set $OmegacompR^d$ into the ball keeping the volume fixed and letting the first eigenvalue and the torsional rigidity respectively decrease and increase. While this does not provide, in general, a $gamma$-continuous map $tmapstoOmega_t$, it can be slightly modified so to obtain the $gamma$-continuity for a $gamma$-dense class of domains $Omega$, namely, the class of polyhedral sets in $R^d$. This allows to obtain a sharp characterization of the Blaschke-Santal'o diagram of torsion and eigenvalue.
2021
Buttazzo, Giuseppe; Pratelli, Aldo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1114773
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